According to John Welch, Benjamin's name is intriguing, although somewhat of a mystery. Benjamin was the name of the younger brother of Joseph (see Genesis 35:18; 46:19), and the tribe of Benjamin was known for being warlike. It is quite possible that Benjamin's name was meaningful to him and his people in the context of his kingship over the land of Zarahemla. This name may have been given to him at birth, or it may have been given to him as a coronation name. Indeed it is probable that Israelite kings were given a new name or a coronation name when they took the throne. Either way, the name of Benjamin was probably meaningful to him as king.
Since the Nephites were from the tribe of Manasseh (see Alma 10:2-3), and since the Mulekites were from the tribe of Judah (as descendants of royal fugitives from Jerusalem and their sailors), it is unclear why Benjamin would have been given the name of the head of another tribe in Israel. Several possibilities exist.
1. The first king over a united Israel was Saul. He was a Benjaminite (see 1 Samuel 9:1) who made the site of Gibeah in the central Benjaminite territory his capital. . . . Similarly, King Benjamin ruled over a newly consolidated kingdom.
2. In ancient Israel the lands of the tribe of Benjamin lay immediately and strategically between the territory of the tribe of Judah to the south and the land of Manasseh to the north. In this central territory the people of Israel "came up" to their judges to be judged (Judges 4:5); here also Samuel assembled all Israel to pray (see 1 Samuel 7:5-6). From traditional functions like these, the name and place of Benjamin symbolized to the Israelites a meeting place between Judah and Manasseh. In Nephite terms, one may conjecture that Benjamin's name . . . could have similarly suggested a middle ground between the Mulekites (of Judah) and the Nephites (of Manasseh).
3. The name Benjamin may mean literally "son of the right hand," although this etymology is not entirely certain. . . . Benjamin promised his people that he who knows "the name by which he is called" "shall be found at the right hand of God" (Mosiah 5:9). Benjamin's audience may well have noticed a similarity between Benjamin's name and this important phrase, "to be found at the right hand of God." [John W. Welch, "Benjamin, the Man: His Place in Nephite History," in King Benjamin's Speech, pp. 25-27]